The behaviors of graph neural networks have been investigated in the context of label homophily for connected node pairs in graphs
[1]}. Label homophily in graphs is typically defined to characterize the similarity of connected node labels in graphs. Here, similar node pair means that the connected nodes share the same label. From the perspective of fairness, we also define the sensitive homophily coefficient to represent the sensitive attribute similarity among connected node pairs. Informally, the coefficient for label homophily and sensitive homophily are defined as the fraction of the edges connecting the nodes of the same class label and sensitive attributes in a graph [2]}, [1]}. We also provide the formal definition as follows:
